Effective seismic force retrieval from surface measurement for SH-wave reconstruction

Convolutional neural network for identifying effective seismic force at a DRM layer for rapid reconstruction of SH ground motions

“…In this section, we compare the inversion performance of the presented data-informed CNN approach with that of the PDE-constrained optimization method shown by Guidio et al 22 We use the test data that correspond to the best and the median performance obtained by the CNNs in Examples 1 and 2 to highlight the differences of the inversion performance between the presented CNN and the PDE-constrained optimization. For each case, we utilize the measured displacement fields of wave motions (𝐮 m ) as input data in the PDE-constrained optimization algorithm, which will identify the target DRM forces.…”

“…Because of its robustness and extensive applicability, the DRM has been widely utilized in numerous research investigations to simulate seismic behaviors in truncated domains. [25][26][27][28][29][30][31][32][33][34][35][36] While the PDE-constrained optimization is highly effective in estimating seismic inputs, in the form of DRM forces, in 2D settings, it is still burdened by time-consuming processes, hindering real time processing, because each inversion simulation typically requires hundreds of forward and adjoint wave simulations in the domain. Such an approach in multidimensional settings would not be a practical, viable tool for rapid reconstruction of wave responses in a domain of interest.…”

“…In other words, when it comes to modeling the wave responses in a truncated domain subject to waves originating from the outside of the domain, such effective seismic nodal forces on a DRM layer drive the wave motions in the domain. Because of its robustness and extensive applicability, the DRM has been widely utilized in numerous research investigations to simulate seismic behaviors in truncated domains 25–36 …”

“…As opposed to the large-scale source-inversion method, this seismic input identification approach only relies on the wave speed data from a near-surface truncated deposit, which can be easily acquired using site characterization techniques like spectral analysis of surface waves (SASW), [13][14][15][16][17] multichannel analysis of surface waves (MASW), 18,19 or full-waveform inversion (FWI). 20,21 Guidio et al 22 presented another method to estimate dynamic nodal forces, which represent arbitrary forms of incoming waves, within a domain reduction method (DRM) layer in a truncated domain by using measurement data. It is noteworthy that the DRM theory was developed by Bielak et al 23 and Yoshimura et al 24 to translate the incoming, incident seismic motions into effective seismic nodal forces on the DRM layer (i.e., virtual interfaces) of a domain of interest.…”

“…Error  in the inverted DRM forces and error  𝑢 in the reconstructed wave responses obtained when using the presented CNN method versus the PDE-constrained optimization approach by Guidio et al22 . It is remarkable that the errors in such an entirely blind test are very small.…”